Aggressive Orders and the Resiliency of a Limit Order Market

Transcription

1 Aggressive Orders and the Resiliency of a Limit Order Market Hans Degryse *,**, Frank de Jong ***, Maarten van Ravenswaaij ****, Gunther Wuyts * This version: * K.U. Leuven, Department of Economics, Naamsestraat 69, 3000 Leuven. ** CentER, P.O. Box 90153, 5000 LE Tilburg *** University of Amsterdam, Finance Group, Roeterstraat 11, 1018 WB Amsterdam. **** SNS Asset Management, Pettelaarspark 70, 5201 DZ s'-hertogenbosch We thank Theo Nijman for comments on an earlier draft as well as seminar participants at the EEA-conference in Venice, CORE, Leuven and Tilburg. The first and last authors gratefully acknowledge financial assistance from FWO-Flanders under contract G Correspondence can be ed to hans.degryse@econ.kuleuven.ac.be.

2 2 Aggressive Orders and the Resiliency of a Limit Order Market Abstract We analyze the resiliency of a pure limit order market by investigating the order flow around aggressive orders (orders that move prices). We explore the issue of resiliency for large and small capitalization stocks as well as stocks with different tick sizes. The impact of aggressive orders is gauged in three complementary ways. First, we look at the order flow before and after aggressive orders. We find strong persistence in the submission of aggressive orders. It takes about 50 subsequent orders before the order flow returns to its unconditional pattern. Second, we describe and estimate the effect of aggressive orders on prices. The estimated price impact is realized quickly. However, due to correlated order flow, prices do move both before and after the submission of aggressive orders. As an explanatory variable, both aggressiveness and order size are important in explaining price effects. Cross-sectionally both firm size and tick size are important in explaining the variation of the impact of order aggressiveness. Small firms exhibit a larger price impact. A larger tick size implies somewhat larger price effects. The spread returns faster to its pre-aggressive level for stocks with a low tick size. JEL Classification: G15 Keywords: aggressive orders, tick size, price impact, depth, order flow, spread

3 3 1 Introduction Throughout the world, there exists a wide diversity of trading systems. In recent surveys of equity markets, Domowitz and Steil (1999) observe that many new trading systems and recently restructured markets apply a limit order design, and Jain (2002) shows that about half of the stock markets throughout the world are organized as a pure limit order book. In such a trading structure, unfilled limit orders are stored in a limit order book, waiting for possible future execution. Given the recent upswing in this type of market, an important question is how efficiently limit order markets operate. The main aspect of the performance of a trading mechanism is its liquidity. In a liquid market, traders do not need to be concerned about the time in between the submission and the execution of their orders, nor about the price impact or execution costs. Harris (1990) distinguishes four dimensions that are associated with liquidity: width (the bid-ask spread for a given number of shares), depth, immediacy and resiliency. Though the literature has already studie d extensively the issue of liquidity, a characteristic of liquidity that has received little attention in empirical research so far is resiliency. It is precisely the resiliency of a limit order market that is the main topic of our paper. Harris defines resiliency as how quickly prices revert to former levels after they change in response to large order flow imbalances initiated by uninformed traders. We apply a slightly broader definition (as in Foucault et al. (2003)) and refer to it as the speed of recovery of the market (in terms of prices, depth and spreads) after a relatively large shock (defined as one that increases the bid-ask spread). In a dealership market, a specialist has an obligation to assure the liquidity of a market in all circumstances, which is cited frequently as one of the important reasons for their presence. In a limit order market, the lack of designated market makers who watch the market continuously may cause illiquidity (and lack of resiliency) in some periods. Depending on the willingness of investors to provide liquidity as if they are market makers, liquidity will vary over time and may even be absent at certain times. A straightforward period for studying liquidity is the time span after an order that widens the bid-ask spread. Although Stigler (1964) already stressed the importance of resiliency, it is a relatively unexplored area in market microstructure research. Exceptions are Bhattacharya and Spiegel (1998) who study trading suspensions on the NYSE and Coppejans, Domowitz and Madhavan (2002), who investigate the resiliency of the Swedish stock index futures market (OMX). The central question of our paper is thus the resiliency of a pure limit order market and its relation with other characteristics. Aggressive orders - orders that induce a large shock

4 4 (defined as one that increases the bid-ask spread) - are the natural candidates to study the resiliency of a limit order market. Our approach adds to the work of Coppejans et al. (2002) who are not specific about the sources of the shocks. We focus on shocks to the bid-ask spread caused by large transactions that consume a significant part of the available liquidity in the book. We relate resiliency to firm characteristics such as market capitalization and tick size, and to the state of the market (spread before the shock). Theory suggests that the order submission behaviour the choice between market orders and limit orders and their aggressiveness may depend on the tick size and the stock s market capitalization (see section 2 of this paper). Our empirical analysis focuses on an eminent example of a limit order market, namely the Paris Bourse (nowadays Euronext Paris). Several aspects of the impact of an aggressive order are studied. First, we examine the relation between aggressive orders and the state of the limit order book. We look at the frequency of the different order types. Also, using conditional probabilities, we look at the order types following an aggressive order. In this way, we can determine whether and how quickly liquidity after an aggressive order is restored. We extend the analysis of Biais, Hillion and Spatt (1995), henceforth BHS95, by not only studying the next order, but also subsequent orders. Secondly, we investigate the market impact of aggressive orders. We test what matters for the price impact of trades: is it the order size of a trade, as most theories of market microstructure assume (see e.g. Easley and O Hara, 1987), or is it only the aggressiveness, i.e. the initial widening of the spread? In a descriptive approach, we directly look at what happens in the limit order book, and more specifically at the best quotes, the depth at the best quotes, the relative spread and the duration between best quote updates. Although the immediate price impact of a trade is a well-studied topic 1, the price effects beyond this immediate price impact are less well investigated. We examine whether aggressive orders have 'long run' price effects. The central hypothesis is that all price effects are incorporated in the first transaction price, as predicted by semi-strong form market efficiency (Glosten and Milgrom (1985)). We also look at how the bid-ask spread and depth at the best quotes develop before and after an aggressive order. These are probably the most direct measures of market resiliency. We investigate how fast spread and depth revert to their pre-aggressive order level. 2 Easley, Keifer and O Hara (1997) show that between transactions, there is a gradual decrease in information asymmetry. Actually, a more general approach would be to study the depth of the market for different order sizes, but data limitations prevent us from doing so. 1 See the pioneering w ork of Glosten and Harris (1988) and the subsequent literature. Hasbrouck (1995) advocates to use Vector Autoregressions for the long run price impacts of trading. 2 Empirically, we capture the normal level of the bid-ask spread by its pre-aggressive order level.

5 5 In addition to this descriptive approach, we also employ a more formal analysis, using regression techniques. In this way, we take into account confounding events, i.e. aggressive orders that arrive shortly after the initial aggressive order. Moreover, in this way we are able to quantify the separate effects that order size and order aggressiveness may have on spread and depth. We study resiliency in two ways, by looking at order flow and price effects. Our findings can be summarized as follows. When considering the relationship between aggressive orders and the order flow, we find as a first result that, in contrast with BHS95, the least aggressive order types turn out to be the most frequent ones, while the most aggressive types are least frequent. Next to looking at unconditional frequencies, it is interesting as well to consider probabilities conditional upon the current order type. We confirm the diagonal effect as reported in BHS95. This means that an order of a given type is likely to be followed by an order of the same type. Moreover, we show that this effect persists over time in the sense that it not only applies to the next order, but also to subsequent orders. Nevertheless, over time conditional probabilities converge to their unconditional levels. Moreover, liquidity is provided to the market when needed. The market impact of aggressive orders is first analyzed using a descriptive approach. We construct a window of 10 updates of the best quotes before and 20 updates after the aggressive order. In this window, we look at the evolution of the best quotes, the depth at the best quotes, the relative spread and the duration between quote updates. Although differences exist between order types and across stocks, we can conclude that the Paris Bourse recovers quickly after an aggressive order since the variables return to their pre-order levels within a few quote updates. These results indicate that the Paris Bourse is a resilient market. Our results also confirm the findings of BHS95 and Hedvall and Niemeyer (1997) who find empirical evidence for the presence of traders watching the limit order book and provide liquidity when spreads are large. We also find evidence of strategic timing of aggressive orders, i.e. fast order submission when the spread is relatively small. Our regression results allow identifying the impact of both order aggressiveness and order size. Market microstructure theories typically only consider order size as a determinant of price impact (see e.g. Easley and O Hara (1987)). We find that order aggressiveness as such and order size on top of order aggressiveness are important in explaining order-to-order returns. The most aggressive orders exhibit the largest price impact. Moreover, the impact of order size of the most aggressive orders is larger than for other order types.

6 6 The remainder of this paper is organized as follows. Section 2 provides an overview of the related literature. Section 3 describes the market structure on the Paris Bourse, the data set and the classification of orders according to aggressiveness. The empirical results are presented in three sections. Section 4 describes the data used in our paper. Section 5 deals with the issue of order aggressiveness and order flow. Section 6 analyzes the impact of aggressive orders on prices as well as on resiliency. Section 7 concludes. 2 Related Literature 2.1 Resiliency and aggressive orders The topic of resiliency of financial markets did not yet receive much attention in the empirical literature. A recent paper that studies resiliency is Bhattacharya and Spiegel (1998), who investigate NYSE trading suspensions. They define resiliency as the ability to absorb very large shocks. A cross-sectional analysis of all trading suspensions during the period shows that the various dimensions of liquidity are substitutes: large cap-stocks have lower bid-ask spreads but halt more often. Our paper focuses on resiliency of a limit order market under less extreme circumstances, i.e. after aggressive orders. Coppejans, Domowitz and Madhavan (2002) study the resiliency of the Swedish stock index futures market (OMX). They find that shocks to depth are restored in less than 60 minutes. These results suggest a self-correcting ability for a stock index futures market. Our paper focuses on shocks that widen the bid-ask spread caused by large transactions that consume a significant part of the liquidity in the limit order book of specific stocks. Biais, Hillion and Spatt (1995) emphasize the interaction between the order book and order flow for the Paris Bourse. They find that aggressive orders consuming liquidity at the quote are followed by new orders within the bid-ask quotes at the other side of the market. We extend the analysis of BHS95 by not only studying the next order, but also subsequent orders. There is an extensive literature on order submission in limit order markets. The pioneering work in this area is by Cohen, Maier, Schwartz and Whitcomb (1981). Recent work includes Hollifield, Miller, Sandas and Slive (2001), who study the order submission on the Vancouver Stock Exchange. Hollifield, Miller and Sandas (2002) provide a theoretical model for the tradeoff between supplying liquidity by issuing a limit order and consuming liquidity by issuing a market order, and test the model on data from the Swedish stock exchange. Griffiths, Smith, Turnbull and White (2000) measure price effects of aggressive orders on the Toronto Stock Exchange from the perspective of the market participant that submitted the

7 7 order. The price effect is measured as the realized price of the order 3 compared to the price immediately prior to the order. They find that only aggressive orders lead to a significantly positive price impact. The price impact of less aggressive orders (e.g. small limit orders or orders that do not generate immediate execution) is small or even negative (conditional on being executed). They find that from the order return perspective, the optimal trading strategy is to buy using limit orders at the bid and to sell using limit orders at the ask. However, this strategy has substantial execution risk. The type of work just discussed requires data on the time to completion of an order. The SBF data set we use does not allow tracking the execution of an order until completion, however. In our paper we therefore take the perspective of the market as a whole (or all the other participants) and look at a short period of time just before and after the submission of the aggressive order. This enables us to investigate whether the market perceives price effects of aggressive orders as correct or whether the market corrects these effects. Apart from the analysis of the resiliency of the market as a whole, our research differs in two other ways from that from Griffiths et al (2000). First, we examine the Paris Bourse, where there is no designated market maker as on the TSE. So our research is one of the first to address these issues for a pure limit order market. 4 Second, our dataset comprises a longer period (six months instead of one). 2.2 Tick size, resiliency and order flow A number of theoretical contributions deal with tick size as a determinant of the order flow composition. We are interested in the dynamics after an aggressive order, as these offer insights about the resiliency of a market. We therefore restrict ourselves to theoretical papers considering sequential price formation. 5 Parlour (1998) shows that systematic patterns in prices and order placement strategies may arise even with only liquidity traders since order placement hinge on past and future expected actions of investors. Aggressive orders will often induce a spread of two-ticks. Parlour (1998) obtains that in a two-tick market it is more likely to see a drop in the ask after a drop in the bid occurred and vice versa. Cordella and Foucault (1999) show that when the bidding process is sequential, there are cases where dealers are better of only undercutting by one tick. This occurs only when the tick size is small. With large tick sizes the wedge between the competitive price and the expected asset value 3 Griffiths et al. (2000) analyze the impact of orders until full completion. 4 On the TSE the market maker only has a limited role compared to e.g. the NYSE specialist. On the one hand his main role is to provide liquidity and thus may improve resiliency to the market. But on the other hand he mainly provides liquidity to small orders and since the focus here is on aggressive orders (which are usually large), his role would have been limited. So whether this difference in market structures will lead to a difference in resiliency between the Paris Bourse and the TSE remains an empirical question. 5 See, for example Seppi (1997) for the effects of tick-size in a static setting.

8 8 increases. Then a dealer can secure a greater profit by posting the competitive price earlier than a competing dealer. This implies that the time to adjust to the competitive price decreases when the tick size increases. Foucault, Kadan and Kandell (2003) measure resiliency by the probability that the spread will reach the competitive level before the next transaction. They show that tick size has implications for the dynamics of the spread in between transactions. In particular, they show that when the tick size is small, traders may find it optimal to undercut or outbid the best quotes by more than one tick in order to speed up execution. This depends on the proportion of patient traders in the population. Ultimately, it is an empirical question how a market s resiliency functions and to what extent its liquidity is re-established after an aggressive order. It is precisely this question that we address in this paper. A number of empirical papers have investigated the impact of tick size changes on market quality. Bacidore (1997), Ahn et al. (1998) and Griffiths et al. (1998) consider the April 1996 reduction in tick size on the Toronto Stock Exchange, while Goldstein and Kavajecz (2000) deal with the changes in tick size and the liquidity provision on the NYSE. Chordia, Roll and Subrahmanyam (2001) study the effect of the reduction in tick size on the NYSE. They show that after the reduction in tick size, the inside spread significantly decreased, but depth at the best bid and ask also decreased. Bourghelle and Declerck (2002) investigate the market quality of the Paris Bourse following the introduction of the Euro. Interestingly, they find that only the depth at the best quotes is significantly affected whereas the spreads remain unaltered. Stocks obtaining a decrease (increase) in tick size experience a decrease (increase) in the depth at the best quotes. 2.3 Firm size, resiliency and order flow Theory also suggests that heterogeneity with respect to firm size is important for resiliency and the composition of the order flow. Empirically, there is a negative relation between firm size and the bid-ask spread (see McInish and Wood (1992), and the review in Madhavan (2000)). Cordella and Foucault (1999) argue that for a given tick size, the speed of adjustment to the competitive quotes must be faster for large firms. Thus large firms should show more resilient markets than small firms. Foucault (1999) shows that when asset volatility increases the proportion of limit orders should increase. The proportion of limit orders for smallcapitalization stocks must be larger than the one for large-capitalization stocks, since volatility is negatively related to equity capitalization (see Hasbrouck (1991)).

9 9 3 Market Structure of the Paris Bourse The Paris Bourse is a computerized limit order market that uses a centralized electronic system, known as CAC (Cotation Assistée en Continu). 6 Similar systems are used in Brussels (NTS), Stockholm (SAX) and Toronto (CATS). The exchange opens at 10:00 a.m. with a batch auction after which a continuous auction takes place until 5:00 p.m. Note that nowadays the exchange opens at 9:00 am and runs until 5:30 p.m., but the times mentioned here were valid during our sample period (March-August 1998). There are no market makers or floor traders. Liquidity is provided by the public limit order book only. A trader can choose between different types of orders. He can submit a limit order, which specifies the quantity to be bought or sold, the price and the date when the order will be withdrawn (unless the order is 'good till cancelled'). A trader can also choose to submit a market order, which only specifies the quantity and direction of the trade and is executed immediately at the best possible price (provided the limit order book is not empty). If the total quantity of the available orders in the limit order book at the best price does not suffice to fill the whole market order, the remaining part of the market order is transformed into a limit order at the transaction price. Hence, market orders do not automatically walk up the limit order book, and do not always provide immediate execution of the whole order. The way of achieving full execution of an order is to use an aggressive limit order, meaning an order that improves the best quotes at the other side of the market and walks up the limit order book. An aggressive limit order therefore provides a faster execution of a large transaction than a market order. Finally, traders can also submit hidden orders, which are limit orders that are not fully visible to other traders. For more details on hidden orders, we refer to BHS95 and D Hondt, De Winne and François-Heude (2002). The price of a limit order can be any price on the pricing grid determined by the tick size. The tick size of a stock depends upon the price level. Stocks with a price below 5 FF have a tick size of 0.01 FF, if the price is between 5 and 100 FF this is 0.05 FF, between 100 and 500 FF it is 0.1 FF and stocks with prices between 500 and 5000 FF have a tick size of 1 FF. For prices above 5000 FF the tick size is 10 FF. 7 This translates into a relative tick size of minimum 0.2% for stocks with the smallest price. Stocks in subsequent price categories have a relative tick size between 1% and 0.05%, 0.1% and 0.02%, and 0.2 and 0.02% respectively. For stocks with prices above 5000 FF, the relative tick size is maximum 0.2%. This is fairly small compared to other exchanges. Until 1997, NYSE used a tick size of 1/8$ for stocks 6 The Paris Bourse merged in 2000 with the Amsterdam Stock Exchange and the Brussels Stock Exchange into Euronext. 7 The tick sizes mentioned are these that were in use during our sample period. After the introduction of the Euro, the tick sizes changed, see Bourghelle and Declerck (2002) for a more detailed discussion.

10 10 above one dollar and 1/16$ for stocks between 0.5$ and 1$, which results in a maximum relative tick size of 12.5%. From 24 June 1997 onwards, the minimum price variation for stocks above one dollar was reduced to 1/16$, resulting in a halving of the maximum relative tick size to 6.25%, which is still considerably larger than on the Paris Bourse. See also e.g. Angel (1997) for a comparison of tick sizes across countries. Shares are traded on a monthly settlement basis. The Société des Bourses Françaises (SBF) acts as a clearing house. The member firms of the Bourse submit orders directly into the CAC system via a local terminal. Transactions occur when the price of a trader hits the quote on the opposite site of the market. Limit orders are stored and executed according to first price priority and then time priority. 8 All market participants can contribute to liquidity by putting limit orders on display. There is some scope for negotiated deals if the limit order book is insufficiently deep. A financial intermediary can negotiate a deal directly with a client at a price within the bid and ask price (also know as the fourchette), provided that the deal is immediately reported to the CAC system as a cross order. For trades at prices outside the fourchette, the member firm acting as a principal is obliged to fill all limit orders displaying a better price than the negotiated price within five minutes. 4 Data Description 4.1 Data Set The sample that is used in this paper consists of 20 stocks listed on the Paris Bourse. These stocks are divided into mutually exclusive groups on the basis of two criteria. First, we distinguish stocks with a small and large market capitalization, where the latter are defined as stocks that are included in the CAC40 index, while the former are not (for more details, see Table 1 and its discussion contained in section 4.2). In the remainder of the text, we will refer to them as small and large stocks, whic h should hence always be read as related to their capitalization. Secondly, as mentioned above, listed stocks differ in their tick size, which in our sample can be 0.1 FF or 1 FF. Hence, in total four groups are obtained, each containing five stocks. Groups 1 and 2 are composed of small stocks with tick size 0.1 FF and 1 FF respectively. The large stocks are placed in group 3 when they have a tick size of 0.1 FF and in group 4, when they have a tick size equal to 1 FF. The sample period ranges from 23 February 1998 until 24 August 1998, which are 123 trading days. We assured that during this sample period the absolute tick size of a given stock is constant, because a varying tick size, 8 Hidden orders loose time priority for the part that is not publicly displayed.

11 11 i.e. a tick size that changes from 0.1 FF to 1 FF or the other way around, might bias our results. The data are taken from the SBF database of the Paris Bourse. Since 1990, the Paris Bourse has set up a database, available on CD-ROM, with detailed information on all kind of securities. For the selected stocks, we use the order file of this database, which contains data on all incoming orders, and the best limit file, which keeps track of all best bid and ask quotes, as well as the depth at this quotes. Our dataset is therefore similar to the one used in Bisière and Kamionka (2000). We eliminated all pre-opening orders from our data set because the trading mechanism during this period, which is a batch auction, differs from the continuous auction setting during the day. For a detailed discussion of the pre-opening period and the opening procedure of the Paris Bourse, see Biais, Hillion and Spatt (1999). A limitation of the SBF data set is that it does not provide information about order cancellations. In other words the data set does not allow to follow orders until completion, as they may be withdrawn or be repriced before (full) execution. However, not observing order cancellations does not hamper our order classification methodology (see section 5), as we take the state of the order book just before the arriving order into account. 4.2 Descriptive Statistics In Table 1, the characteristics of the different groups of stocks, their composition and some descriptive statistics of the data are presented. First, the minimum, maximum and average best ask quotes are given. Notice that for small tick stocks, these are located between 100 and 500 FF, while for stocks with a large tick size these are above 500 FF. This ensures the same tick size over the sample period. Also, the average depth at the best quotes is shown. For a majority of the stocks the depth at the best bid is smaller than the depth at the best ask. Also, in general, the depth in number of shares is smaller for small stocks than the depth for large stocks. Next, the average ask returns and their standard deviation are calculated. For a majority of the stocks, the average daily return is negative. The standard deviation is smaller for stocks with the large tick size. Subsequently, the average and median bid-ask spread, expressed in FF, are shown, as well as the proportion of the time the spread was 0, 1, 2, ticks. A remarkable result is that for stocks with a small tick size (0.1 FF), the proportion of spreads larger than 5 ticks is more than 50%, while for large tick stocks there is a large proportion of 1 or 2 tick spreads. This might be an indication that for stocks with a tick size of 1 FF, this minimum price variation is often a binding constraint, while this is not the case for the small tick size. The average relative spread (the ratio of average spread and average

12 12 midquote) is larger for small stocks. Given the size of the stock, the differences between tick sizes are on average small. The last rows of Table 1 provide details on the market capitalization of the stocks and the average daily traded volume (in million FF), as well as their position in the ranking of French stocks. It shows that the stocks in our sample are distributed across different quintiles on the Paris Bourse, meaning that we are indeed analyzing different groups of stocks. PLEASE INSERT TABLE 1 AROUND HERE 5 Order aggressiveness and order flow 5.1 Order classification methodology and frequency of order types In order to characterize the order submission behavior, all incoming orders are classified according to the scheme proposed BHS95 and also used in other papers, see e.g. Bisière and Kamionka (2000). A distinction between orders is made on the basis of the direction of the order (buy or sell), and of its aggressiveness. The classification of buy orders is depicted by Figure 1. Buy orders are classified into aggressiveness order types 1 to 6, where 1 is the most aggressive buy order type, and 6 is the least aggressive. An order of type 1 is an order to buy a larger quantity than is available at the best ask at a price that is higher than the best ask. This means that these orders walk up the limit order book and result in multiple trades. An order of type 2 is an order for a larger quantity than available at the best ask, but that does not walk up the limit order book above the best ask. The reason for this can be twofold. First, the order can be a limit order with a price equal to the best ask, but with a larger quantity than the depth at the best ask. Secondly, the order can be a market order which has an order size larger than the one available at the best price. In the latter case, the rules of the Paris Bourse forbid such market order to walk up the limit order book. For both, the part of the order that is not executed immediately is converted into a limit buy order. Orders of type 3 are orders to buy a quantity that is lower than the one offered at the best ask, hence they result in full and immediate execution. In contrast, the remaining buy order types are not executed immediately, so they do not result instantaneously in a transaction. Type 4 orders have a price worse than the best ask, but better than the best bid price, while type 5 orders have a price exactly at the best bid. The remaining orders are collected in type 6. Sell orders are classified in a symmetric way, resulting in order types 7, the most aggressive sell order, to 12, which is the least aggressive sell order type.

13 13 PLEASE INSERT FIGURE 1 AROUND HERE On both sides of the market, the most aggressive order types immediately result in transactions and cause a price movement. Less aggressive order types, such as 3 and 9, still result in transactions, but do not give rise to an update of the best quotes. They only reduce the depth at the best ask and bid respectively. The sum of these three types of orders is a proxy for market orders as in Foucault (1999). Order types 4 and 5, and 10 and 11 do not give rise to transactions while the prices of the least aggressive orders 6 and 12 are even worse than the current best quotes in the market. Since the focus of this paper is on aggressive orders, our attention will mainly go to the two order types on each side of the market that are most aggressive, being types 1 and 2 for buy orders and 7 and 8 for sell orders. The frequency of order types is documented in Table 2. This frequency table shows that the least aggressive order types (6 and 12) have the highest frequency of occurring, followed by types 3 and 9. On the other hand, the most aggressive order types (1 and 7) have the lowest probability of occurring. Somewhat less aggressive orders (types 2 and 8) however have already a much higher frequency. The results are similar for buy and sell orders. PLEASE INSERT TABLE 2 AROUND HERE BHS95 also report that the most aggressive order types are most infrequent, but some of their other results are different from ours. In BHS95, type 3 and 9 orders are most frequent, while type 2 and 8 are much more infrequent than in our results. Griffiths et al. (2000) report frequencies for the Toronto Stock Exchange (TSE). They also find that types 3 and 9 are most frequent and types 1 and 7 most infrequent. However, in contrast with BHS95, and in accordance with our results, they also find that type 2 and 8 orders are much more frequent than 1 and 7. On TSE, types 1 and 7 are even more infrequent than on the Paris Bourse. One possible explanation is that some TSE stocks have bid-ask spreads equal to the tick size. This drives traders to trade at the best quotes because they cannot improve the quotes. This may explain why a larger fraction of type 3's (small market orders) and a smaller fraction of type 4's are observed. The results given above apply to all groups of stocks, but nonetheless there are also some notable differences between groups. Although infrequent in all groups, types 1 and 7 are most infrequent in groups with a large tick size (groups 2 and 4). On the other hand type 2 and 8 are more frequent in the large tick size groups than in groups with a small tick size.

14 Conditional probability of order types The results in Table 2 are unconditional probabilitie s. In order to analyze the influence of aggressive orders on the subsequent order flow, we turn in this section to conditional probabilities. Table 3 presents the probabilities that the next order is of a certain type, conditional upon the aggressiveness type of the current order. To conserve space, and as the results do not differ dramatically across groups of stocks, we present unweighted averages in Table 3. In the table, each element can be interpreted as the probability that a current order of the type given by the row is followed by an order of the type given by the column. The last row presents the unconditional probabilities of the type given by the column. The last two columns show the probabilities that an order of the type given by the row is followed by respectively a buy order or sell order. PLEASE INSERT TABLE 3 AROUND HERE We find that the probability that an order of a certain type is followed by an order of the same type is relatively high. This is indicated by the fact that the elements on the diagonal of the table are in almost all cases the highest in the column. This is a confirmation of the diagonal effect, also found in other studies (e.g. BHS95). The diagonal effect may result from strategic order splitting strategies, imitating behavior, or similar reactions to events by market participants. The last two columns in each panel show that buy orders are more likely to be followed by buy orders, while sell orders are more likely followed by sell orders. This is in line with Parlour (1998) who showed that systematic patterns in order placement strategies might arrive. Finally, in all panels, there is high probability that an order of type 1 is followed by an order of type 4. i.e. an aggressive order is often followed by a price improving limit order on the same side of the market. This result is in correspondence with BHS95. It shows that new liquidity is provided to the market after it has been consumed. Of course, another explanation for this pattern might be that it is the result of traders that are splitting orders. A similar result holds for sell orders: the probability that an order of type 7 is followed by an order of type 10 is relatively high. The bid-ask spread widens after an aggressive buy or sell order (type 1 or 7). Since limit order traders can earn this spread, there is an increased incentive to provide new liquidity within the best bid-ask quotes. In Table 3, we looked at the first order following an aggressive order. An interesting extension is to study also subsequent orders. In Figure 2, the evolution of the diagonal effect over time is drawn. More specifically, the probability is given that an order of type i, i = 1..12, at time t is followed by an order of the same type i at time t+k, k = We find that the

15 15 diagonal effect persists beyond one order. But the conditional probabilities do converge to the unconditional levels. Remarkable is also the difference between orders of type 4 and 10 and other types. The probability that an order of these types is followed by an order of the same type is relatively small, compared with the other order types. Often further undercutting becomes impossible and the provided liquidity needs to be consumed first before similar order types become possible. The next order that again provides liquidity within the quotes will only be some orders later. For this reason, convergence for these types is not as pronounced as for the other types. The (not reported) differences between groups show that the convergence to the unconditional levels is smoother for large stocks than for small stocks and occurs slightly faster for the smaller stocks for the more aggressive order types. Furthermore, there is only a small difference between groups with different tick sizes, taking capitalization as given. Important in the interpretation of Figure 2 is that the x-axis is expressed in order time and not in calendar time. This means that although convergence is faster for smaller stocks when expressed in order time, this is not necessarily the case when expressed in calendar time. In calendar time convergence will be even faster for large stocks, the intuitive reason for this being that orders for smaller stocks occur less frequently than for large stocks, i.e. the average duration between orders is much smaller for large stocks. PLEASE INSERT FIGURE 2 AROUND HERE 6 Market impact of aggressive orders 6.1 Descriptive approach As a first step in analyzing the market impact of aggressive orders, we employ a descriptive, event study type of approach. To study resiliency, we look directly at what happens in the limit order book in a small period of time around an aggressive order. The advantage of this methodology is that we describe what in reality is going on in the limit order book. The results of this descriptive approach are presented in Figure 3. Panel A of Figure 3 starts from an order of type 1. A window around the submission of such order is created. More specifically, we consider a window of 10 updates of the best quotes (prices or depth or both)

16 16 before and 20 updates after the submission. Within each window, the best quotes, the depth at the best quotes, the relative spread and the duration between best quote updates are studied. Important in the interpretation of the figures is that the values of the variables are calculated relative to the value at the time of the submission of the order of type 1, which was set equal to 100. This implies that the lines express how the variable changed compared to time zero, the time of the aggressive order. Moreover, the results are presented in order time. To have an idea about the effect in calendar time, one can use the average duration between quote updates. This average duration is 84 seconds for group 1, 100 seconds for group 2, 45 seconds for group 3 and 34 seconds for group 4. From this, it can be derived that a 20 period interval after the aggressive order, will on average comprise a period ranging between about 33 minutes for stocks of group 2 and 11 minutes for group 4. Finally, the means across the stocks within the different groups are plotted. Panels B, C and D show the results starting from order types 2, 7 and 8 respectively. In the subsequent discussion of Figure 3, we will compare the effects across different order types (see the different panels) and across stocks (see the different rows within a panel). Notice that by looking at what happens before and after the submission of aggressive orders, we generalize the BHS95 analysis to order submission behavior. They find shifts in both bid and ask quotes after large transactions. PLEASE INSERT FIGURE 3 AROUND HERE We start our discussion of the results by looking at the evolution of the best quotes (prices). As a consequence of the definitions used in the classification of orders, the ask moves up after the most aggressive buy order. Indeed, we see that the best ask, given by the dashed line, jumps up after an order of type 1. The largest effect is found for groups 1 and 2, which are the small stocks. The best bid, drawn in full lines, increases as well, but there is no jump. The mirror image is obtained for the most aggressive sell orders: the bid jumps down, while the ask does not, although the latter decreases as well after the order, but in a more gradual way. Again the effects are more pronounced for smaller stocks. The ask price jumps upwards after a less aggressive buy order (type 2), but now also the bid jumps, but less strongly than the ask. The intuition for the difference in results between the two most aggressive order types is that the unexecuted part of order type 2 pops up at the other side of the market inducing an immediate shift in the bid. Again, the jumps are the largest for small stocks. However, the magnitude of the effect is also larger after a type 2 order than after a type 1 order. After less aggressive sell orders (type 8), the jump in the bid is much smaller and also the subsequent decrease is smaller than after type 7 orders.

17 17 Note that our measure of price impact is computed in the time window around the aggressive order and thus describes the immediate market impact of the aggressive order. In this way, it differs from the methodology in Griffiths et al. (2000), who use the fill price of an order in their computation of price impact. Given that an order may be filled over time, their measure computes price impact from the trader's viewpoint, while ours measures the immediate price impact from the market's perspective. The order of magnitude of the price impacts found by Griffiths et al. (2000) is similar, however. Recall also that the prices are presented as the change with respect to time zero, when the aggressive order was submitted. Because of this, it is not disturbing that the line for the best bid is in some cases above the line of the best ask, this just means that the bid changed less heavily than the ask compared to the reference point in case of a price drop, or that the bid changed more than the ask in case of a price increase. Now we turn to the evolution of the depth at the best quotes around an aggressive order. The depth at the best ask is given by the dashed lines in Figure 3, second column, the depth at the best bid by the solid lines. The depth sharply decreases until the moment that an aggressive order is submitted. After such an order, the depth strongly increases again, an effect that is most pronounced for large stocks. In contrast with the results for the best quotes, there are considerable differences in the depth between buy and sell orders since after an aggressive buy order (type 1 and 2): the increase in the depth is about five times larger than after an aggressive sell order (type 7 and 8). In addition to the direction of an order, the tick size matters: given the size of a stock, the effect on the depth is stronger for stocks with a larger tick size. Finally, remark that the evolution of the depth at the best ask does not differ much from the evolution at the best bid. These results suggest that shocks to depth from aggressive orders are restored quickly. In a final point in this section, we investigate if traders who use aggressive orders try to minimize their price impacts by timing their trades. Timing in aggressive order submission can be examined by looking at the spreads and the durations around the submission of the aggressive order. In Figure 3, the relative spread is drawn, which is defined as the difference between the bid and ask, divided by the midquote. On average, the relative spread before an aggressive order decreases. At this point, aggressive orders are submitted quickly, as can be seen from the fact that the average duration between best quote updates is much shorter around an aggressive order. Griffiths et al. (2000) find a positive relation between the bid-ask spread and the aggressiveness of the order but do neither report how much smaller the spread is before its submission nor do they look at durations. After an aggressive order, the spread increases again, not only the next order, but also some orders further into the future. An

18 18 explanation for this fact lies in the persistence in the order flow (the diagonal effect) discussed in section 5. Some more observations can be made from the different panels of Figure 3. First, it can be seen that the order of magnitude of the movement in the relative spread is increasing in order aggressiveness: the effect is stronger for an order of type 1 (type 7) than for an order of type 2 (type 8). When taking the size of a stock as given, the relative spread moves more heavily for stocks with a small tick size, this property is even more pronounced for buy orders than for sell orders. For the duration between best quote updates, similar inferences can be made. The duration is more volatile after an aggressive order than before. Moreover, the largest effect is found for the most aggressive order types (type 1 and 7), it is about two times larger than for less aggressive orders (type 2 and 8 respectively). The movement in duration is decreasing in stock size, since it moves more heavily for small stocks (groups 1 and 2). Finally, because the duration of stocks with a small tick size moves stronger than the duration of stocks with a large tick size, we find that duration is also decreasing with tick size. Briefly summarizing the findings in this section, we can state that there are, sometimes even large, effects around an aggressive order, but that the market recovers quickly after an aggressive order. After an aggressive order, the levels of the best quotes, the depth at the best quotes, the relative spread and the duration between quote updates return to their levels before such order within a few quote updates 9. Hence, despite the fact that there are no market makers who monitor the market and have an obligation to provide liquidity at all times, our results suggest that the Paris Bourse is a resilient market. Of course, the descriptive approach in this section might be subject to a classic problem in event studies: the issue of confounding events. This means that in the time span around an order of a certain type, another order of the same type might occur. This complicates the analysis of the effect of a specific order type since it is difficult to attribute the change in the order book to a certain order. Furthermore, there is likely to be noise in the data. Therefore, in the next section, we further explore this issue in a more formal way, that allows us to correct for both persistence on the order flow and noise. More precisely, we will use different regression models to assess the impact of aggressive order. 9 Recall that Figure 3 is expressed in order time. One could however use the average durations between quote updates mentioned earlier in this section to obtain an idea of the c alendar time.

19 Analytical approach In this section, we complement the event study of the previous section by means of an analytical approach. This allows us to accommodate for some drawbacks of the descriptive approach. In addition, in this section we will separate the impact of an aggressive order in itself and order size, following among others Easley and O Hara (1987), who show that order size is important in determining price impacts. Another reason for disentangling both is that aggressive orders have on average a larger order size Impact on order to order ask return In a first regression, we estimate the price impact of various types of orders. To avoid problems of nonstationarity, we use the percentage return on the best ask after the order, which we denote by R t. The order type is included as an explanatory variable. More precisely, for each order type a we incorporate a dummy variable D a,t-l which is one if the order at time t-l is of type a, with a A = {1, 2,, 11}. So A is the set of order types, excluding the last order type to avoid perfect multicollinearity in estimation. A second variable that may influence the price impact is the order size, which is confirmed by Griffiths et al. (2000). Hence, we add this as an independent variable defining order size in number of stocks. Moreover, order size enters the regression in a positive way for buy orders and in a negative way for sell orders. Finally, we also allow the impact of order size to be conditional on the type of order that was submitted by including interaction terms. To account for dynamic effects, we not only consider current values of the variables, but also lags. Bringing all these elements together, we get the following equation that will be estimated: R t = α + + L l= 0 A a= 1 l= 0 l L φ R β t 1 l a, l D + ε a, t l t + L γ Ordersize + l t l l= 0 a= 1 l= 0 A L δ a, l D a, t l Ordersize t l (1) The coefficients to be estimated are α, β a,l, γ l, δ a,l and φ l. Remark that also lagged returns are included to capture the dynamics of returns in a better way. In the reported estimations we included one lag of each variable, so L is set equal to one. Finally, ε t is the error term which is assumed to be i.i.d.(0,σ ²). The coefficients β a,0 capture the price impact of a specific order type as such compared to the base (order type 12). The coefficient γ l represents the impact of an increase in one unit of order size for type 12. Finally, the sum of γ l and δ a,l gives the impact of order size of a certain order type. Assuming that price impacts of aggressive orders are

20 20 equally distributed throughout the day there is no need to include order submission time in the model. The model is estimated for each of the four groups using OLS. We used the 95 % percentile for order size to avoid biasing our results by a few outliers 10. Hausman et al. (1992) use a similar approach for order volume, but use the 99.5% percentile. The regression results are reported in Table 4, significant coefficie nts at the 5% level are indicated in bold. PLEASE INSERT TABLE 4 AROUND HERE We clearly find that the return on the best ask is influenced by the order type, since most coefficients of the current order-dummies are significant. The effect is largest for the most aggressive buy orders, followed by type 2 orders. Comparing across groups, aggressive orders have the largest impacts for small stocks (groups 1 and 2). When taking the size of the order as given, and in general the effect of the most aggressive orders is larger for stocks with a larger tick size. Moreover, not only the current order has an influence on the return, also the type of the previous order is significant, although its impact is smaller. This is not surprising given the persistence in order flow found earlier. Remark however that while the signs of the most aggressive buy orders (type 1 and 2) are the same as their lags, this is no longer true for aggressive sell orders (type 7 and 8), the dummies have a negative sign, but their lags have a positive sign. Order size for the base case, order type 12, has a negative sign meaning that larger orders have a more negative return. This effect is again stronger for smaller stocks. Finally, we also find that the interaction terms are significant. Almost all have a positive sign, indicating that a given order type has a stronger effect on the return on the best ask if the order size of that order is larger. This result is in line with theoretical predictions (see e.g. Easley and O Hara (1987) and previous findings (see e.g. de Jong, Nijman and Roëll (1995)). To assess the economic impact of orders of various types and sizes, we calculated their implied impact on the ask return based on the estimates reported in Table 4. The results are reported in Table 5. This table displays the implied impact of order size for the aggressive orders types 1 and 2. The left column shows the impact of the aggressive order as such, i.e. for a very low order size. The magnitudes can be inferred from the coefficients β 1,0 and β 2,0 reported in Table 4. We learn that order aggressiveness as such determines order returns. For example, an order type 1 in group 1 induces an increase of about 8 basispoints (0.08%). We learn that the impact of order type 1 is larger than order type 2. Moreover, market capitalization and tick size matter. In particular, small stocks and stocks with larger tick size 10 This means that if the order size of an order exceeds the 95 % percentile of the empirical distribution of order size for a stock, we set the order size equal to the 95 % percentile.